Balance multicomponent steady-state mass

Example 1 Multicomponent Mass and Enthalpy Balances at steady-state. 

Multicomponent rectification Consider a multicomponent mixture of m-species continuously fed into a distillation column (Acrivos and Amundson, 1955 Amundson, 1966 Ramkrishna and Amundson, 1985). Let and be the compositions of the ith species on the nth plate for the liquid phase and the vapor phase, respectively. Based on constant molal overflow of liquid with a downflow rate L and a vapor upward flow rate V, the steady-state mass balance for the ith species in the rectifying section above the nth plate leads to the equation... 

The mass balance equations of the traditional multicomponent rate-based model (see, e.g., Refs. 57 and 58) are written separately for each phase. In order to give a common description to all three considered RSPs (where it is possible, of course) we will use the notion of two contacting fluid phases. The first one is always the liquid phase, whereas the second fluid phase represents the gas phase for RA, the vapor phase for RD and the liquid phase for RE. Considering homogeneous chemical reactions taking place in the fluid phases, the steady-state balance equations should include the reaction source terms ... 

The component mass balance equations of the traditional multicomponent rate-based model (see, e.g., Refs. [15, 16]) are written separately for each phase. As chemical reactions take place in the fluid phases, the steady-state balance equations should include the reaction source terms ... 

The state of the art procedure for design of cyclic PSA or TSA processes using activated carbon adsorbents is to simultaneously solve the partial differential equations describing the mass, the heat, and the momentum balance equations for each step of the process using the appropriate initial and boundary conditions. These numerical calculations are carried out over many cycles for the process until a cyclic steady-state performance solution is achieved. Many different numerical integration algorithms are available for this purpose. The core input variables for the solution are multicomponent gas adsorption equilibria, heats, and kinetics for the system of interest [37]. 

---